Significant Figures and Scientific Notation

Physics 11 In both physics 11 and physics 12, we use significant figures in our calculations. On tests, assignments, and labs students are expected to answer questions with the correct number of significant figures. Typically, 1 point on every assessment is given directly to sig figs. Scientific notation is one way that scientists show sig figs easily.

Sig Figs We have to look at significant figures because the precision of all measuring devices is limited. Therefore, the number of digits that are valid is also limited. The valid digits are called the significant digits. - They are the digits you are sure of and one estimated digit.

Sig Figs (Summary) We use significant figures to indicate the PRECISION of the measuring tool. Significant figures indicate include all the digits that can be directly measured and one that is ESTIMATED.

Sig Figs (Summary) RULES FOR DETERMINING HOW MANY SIG FIGS THERE ARE: 1. Nonzero digits are always significant. Ex: sig figs 2. All final zeros after the decimal point are significant (if they are to the right of a nonzero digit). Ex: sig figs 3. Zeros between two other significant digits are always significant. (captive) Ex: sig figs 4. Zeros used solely for spacing the decimal point are not significant. (place holders) UNLESS THERE IS A DECIMAL AFTER Ex: sig figs Ex: sig figs

Examples 1) (5 sig figs) 2) 43.00(4 sig figs) 3) (5 sig figs) 4) (3 sig figs) 5) 302 (3 sig figs) 6) (2 sig figs) 7) 320(2 sig figs) 8) 320.(3 sig figs)

Scientific Notation (Summary) 1 digit before decimal (can’t be 0) Always ends with x10… If the exponent is positive, the number is LARGE and vice versa The number of digits in a scientifically noted measurement is the number of sig figs

Examples Change these from scientific notation into regular number notation –5.6 x 10 4 – x Change these into scientific notation: –135.9 cm –0.89 m

Complete questions a, b, c on Significant Digits Worksheet

Operations with Sig Figs * the result of any mathematical operation with measurements can never be more precise than the least precise measurement.

Addition and Subtraction * Use the least number of decimals.

Multiplication and Division After performing the calculation, note the factor with the least number of significant figures. Round the answer to this number of digits m ÷ s =  2.02 m/s

From now on… (Summary) In physics, just use the rule: –Sig Figs = least number of sig figs in the question measurements. –REMEMBER: If something is a constant or counted, this is not included in sig fig calculations. –WHY? –Don’t round until the end of the problem (keep at least 4 decimals if you do need to round) –Use the ANSWER button on your calculator

Complete side 2 of Sig Figs Worksheet